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solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 411px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 205.5px; transform-origin: 407px 205.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis square is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the square, determine the x coordinate of the line that splits the regions. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 7 to 11, then these two numbers will be the first two numbers in the input. The last entry is the side of the square.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = ratio_polygon(s)\r\n  y = s;\r\nend","test_suite":"%%\r\ns=[1 4 10];\r\ny=ratio_polygon(s);\r\ny_correct=2;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[1.5 4 10];\r\ny=ratio_polygon(s);\r\ny_correct=2.7273;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[7 3 11.3];\r\ny=ratio_polygon(s);\r\ny_correct=7.91;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[121 125 17.37];\r\ny=ratio_polygon(s);\r\ny_correct=8.5438;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[19 3 25];\r\ny=ratio_polygon(s);\r\ny_correct=21.5909;\r\nassert(abs(y-y_correct)\u003ceps)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":76,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-21T18:12:43.000Z","updated_at":"2026-03-24T12:20:14.000Z","published_at":"2021-01-21T18:12:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a square sitting in Quadrant I as depicted in an example below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"282\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"287\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis square is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the square, determine the x coordinate of the line that splits the regions. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 7 to 11, then these two numbers will be the first two numbers in the input. The last entry is the side of the 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Circle","description":"Consider a circle which has been divided into three concentric circles as depicted in the figure below\r\n\r\nThe ratio betwen the areas of the inner, intermediate, and outer regions is given in the input. The outermost radius is 1. Given the ratio of the regions, please determine the radii of the inner and intermediate regions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 439.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 219.75px; transform-origin: 407px 219.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 315px 8px; transform-origin: 315px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider a circle which has been divided into three concentric circles as depicted in the figure below\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 358.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 179.25px; text-align: left; transform-origin: 384px 179.25px; white-space: pre-wrap; margin-left: 4px; 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data-image-state=\"image-loaded\" width=\"359\" height=\"353\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377px 8px; transform-origin: 377px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe ratio betwen the areas of the inner, intermediate, and outer regions is given in the input. The outermost radius is 1. Given the ratio of the regions, please determine the radii of the inner and intermediate regions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = circle_split(s)\r\n  y = s;\r\nend","test_suite":"%%\r\ns=[1 1 1];\r\ny=circle_split(s);\r\ny_correct=[0.5774 0.8165];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[1 2 3];\r\ny=circle_split(s);\r\ny_correct=[0.4082 0.7071];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[3 2 1];\r\ny=circle_split(s);\r\ny_correct=[0.7071 0.9129];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[5 5 1];\r\ny=circle_split(s);\r\ny_correct=[0.6742 0.9535];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[4 4 0];\r\ny=circle_split(s);\r\ny_correct=[0.7071 1.0000];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":"2021-12-26T14:39:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-22T23:01:39.000Z","updated_at":"2025-12-27T03:30:53.000Z","published_at":"2021-01-22T23:03:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a circle which has been divided into three concentric circles as depicted in the figure below\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"353\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"359\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe ratio betwen the areas of the inner, intermediate, and outer regions is given in the input. The outermost radius is 1. Given the ratio of the regions, please determine the radii of the inner and intermediate 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Hexagon - Problem the third","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 402px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 201px; transform-origin: 407px 201px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a hexagon sitting in Quadrant I as depicted in an example below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 279px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 139.5px; text-align: left; transform-origin: 384px 139.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis hexagon is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the hexagon, determine the radius of the circle that splits the region. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 1 to 2, then these two numbers will be the first two entries in the input. The last entry is the side of the hexagon.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = ratio_polygon(s)\r\n  y = s;\r\nend","test_suite":"%%\r\ns=[1 2 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.5250;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[0 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[1 7 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.3215;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[3 7 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.4981;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[4 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.8134;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[3 5 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.5569;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-22T22:23:48.000Z","updated_at":"2025-12-27T03:32:18.000Z","published_at":"2021-01-22T22:24:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a hexagon sitting in Quadrant I as depicted in an example below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"273\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"307\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis hexagon is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the hexagon, determine the radius of the circle that splits the region. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 1 to 2, then these two numbers will be the first two entries in the input. The last entry is the side of the 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Square - Problem the first","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 411px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 205.5px; transform-origin: 407px 205.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a square sitting in Quadrant I as depicted in an example below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 288px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 144px; text-align: left; transform-origin: 384px 144px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis square is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the square, determine the x coordinate of the line that splits the regions. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 7 to 11, then these two numbers will be the first two numbers in the input. The last entry is the side of the square.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = ratio_polygon(s)\r\n  y = s;\r\nend","test_suite":"%%\r\ns=[1 4 10];\r\ny=ratio_polygon(s);\r\ny_correct=2;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[1.5 4 10];\r\ny=ratio_polygon(s);\r\ny_correct=2.7273;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[7 3 11.3];\r\ny=ratio_polygon(s);\r\ny_correct=7.91;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[121 125 17.37];\r\ny=ratio_polygon(s);\r\ny_correct=8.5438;\r\nassert(abs(y-y_correct)\u003ceps)\r\n%%\r\ns=[19 3 25];\r\ny=ratio_polygon(s);\r\ny_correct=21.5909;\r\nassert(abs(y-y_correct)\u003ceps)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":76,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-21T18:12:43.000Z","updated_at":"2026-03-24T12:20:14.000Z","published_at":"2021-01-21T18:12:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a square sitting in Quadrant I as depicted in an example below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"282\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"287\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis square is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the square, determine the x coordinate of the line that splits the regions. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 7 to 11, then these two numbers will be the first two numbers in the input. The last entry is the side of the 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Circle","description":"Consider a circle which has been divided into three concentric circles as depicted in the figure below\r\n\r\nThe ratio betwen the areas of the inner, intermediate, and outer regions is given in the input. The outermost radius is 1. Given the ratio of the regions, please determine the radii of the inner and intermediate regions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 439.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 219.75px; transform-origin: 407px 219.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 315px 8px; transform-origin: 315px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider a circle which has been divided into three concentric circles as depicted in the figure below\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 358.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 179.25px; text-align: left; transform-origin: 384px 179.25px; white-space: pre-wrap; margin-left: 4px; 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data-image-state=\"image-loaded\" width=\"359\" height=\"353\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377px 8px; transform-origin: 377px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe ratio betwen the areas of the inner, intermediate, and outer regions is given in the input. The outermost radius is 1. Given the ratio of the regions, please determine the radii of the inner and intermediate regions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = circle_split(s)\r\n  y = s;\r\nend","test_suite":"%%\r\ns=[1 1 1];\r\ny=circle_split(s);\r\ny_correct=[0.5774 0.8165];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[1 2 3];\r\ny=circle_split(s);\r\ny_correct=[0.4082 0.7071];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[3 2 1];\r\ny=circle_split(s);\r\ny_correct=[0.7071 0.9129];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[5 5 1];\r\ny=circle_split(s);\r\ny_correct=[0.6742 0.9535];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n%%\r\ns=[4 4 0];\r\ny=circle_split(s);\r\ny_correct=[0.7071 1.0000];\r\nassert(all(abs(y_correct-y)\u003c1e-5))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":"2021-12-26T14:39:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-22T23:01:39.000Z","updated_at":"2025-12-27T03:30:53.000Z","published_at":"2021-01-22T23:03:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a circle which has been divided into three concentric circles as depicted in the figure below\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"353\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"359\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe ratio betwen the areas of the inner, intermediate, and outer regions is given in the input. The outermost radius is 1. Given the ratio of the regions, please determine the radii of the inner and intermediate 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Hexagon - Problem the third","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 402px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 201px; transform-origin: 407px 201px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a hexagon sitting in Quadrant I as depicted in an example below:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 279px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 139.5px; text-align: left; transform-origin: 384px 139.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis hexagon is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the hexagon, determine the radius of the circle that splits the region. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 1 to 2, then these two numbers will be the first two entries in the input. The last entry is the side of the hexagon.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = ratio_polygon(s)\r\n  y = s;\r\nend","test_suite":"%%\r\ns=[1 2 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.5250;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[0 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[1 7 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.3215;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[3 7 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.4981;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[4 1 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.8134;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n%%\r\ns=[3 5 1];\r\ny=ratio_polygon(s);\r\ny_correct=0.5569;\r\nassert(abs(y-y_correct)\u003c5e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-22T22:23:48.000Z","updated_at":"2025-12-27T03:32:18.000Z","published_at":"2021-01-22T22:24:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a hexagon sitting in Quadrant I as depicted in an example below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"273\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"307\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis hexagon is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the hexagon, determine the radius of the circle that splits the region. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 1 to 2, then these two numbers will be the first two entries in the input. The last entry is the side of the 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